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Sum of series/ 2i+1/n

Sum of series 2i+1/n

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  oo           
 ___           
 \  `          
  \   /      1\
   )  |2*i + -|
  /   \      n/
 /__,          
i = 1

\sum_{i=1}^{\infty} \left(2 i + \frac{1}{n}\right)

Sum(2*i + 1/n, (i, 1, oo))

The radius of convergence of the power series

Given number:

2 i + \frac{1}{n}

It is a series of species

a_{i} \left(c x - x_{0}\right)^{d i}

- power series.
The radius of convergence of a power series can be calculated by the formula:

R^{d} = \frac{x_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}

In this case

a_{i} = 2 i + \frac{1}{n}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{i \to \infty} \left|{\frac{2 i + \frac{1}{n}}{2 i + 2 + \frac{1}{n}}}\right|

True

False

The answer [src]

     oo
oo + --
     n

\infty + \frac{\infty}{n}

oo + oo/n